After 9'O clock at what time between 9 p.m. and 10 p.m. will the hour and minute hands of a clock point in opposite direction?

Hour hand's speed is $$\frac{1}{2} ^o$$ per min.
And minute hand's speed is $$6^o$$ per minute
So relative speed of minute hand will be $$6^o$$ - $$\frac{1}{2} ^o$$ = $$\frac{11}{2}$$ per minute
Hence time taken to make an angle of $$180^o$$ in between will be = $$\frac{90}{\frac{11}{2}}$$ (As at 9:00 o'clock angle between them is already $$90^o$$ )
So time will be $$\frac{180}{11}$$ minutes passed 9